The present invention relates in general to cryptography and secure communication via computer networks or via other types of systems and devices, and more particularly to hierarchical, identity-based schemes for encrypting and decrypting communications.
Roughly speaking, identity-based cryptosystems are public key cryptosystems in which the public key of an entity is derived from information associated with the entity's identity. For instance, the identity information may be personal information (i.e., name, address, email address, etc.), or computer information (i.e., IP address, etc.). However, identity information may include not only information that is strictly related to an entity's identity, but also widely available information such as the time or date. That is, the importance of the concept of identity information is not its strict relation to the entity's identity, but that the information is readily available to anyone who wishes to encrypt a message to the entity.
An entity's private key is generated and distributed by a trusted party or logical process, typically known as a private key generator (“PKG”). The PKG uses a master secret to generate private keys. Because an entity's public key may be derived from its identity, when Alice wants to send a message to Bob, she does not need to retrieve Bob's public key from a database. Instead, Alice merely derives the key directly from Bob's identifying information. Databases of public keys are unnecessary. Certificate authorities (“CAs”) also are unnecessary. There is no need to “bind” Bob's identity to his public key because his identity is his public key.
The concept of identity-based cryptosystems is not new. It was proposed in A. Shamir, Identity-Based Cryptosystems and Signatures Schemes, ADVANCES IN CRYPTOGRAPHY—CRYPTO '84, Lecture Notes in Computer Science 196 (1984), Springer, 47-53. However, practical identity-based encryption schemes have not been found until recently. For instance, identity-based schemes were proposed in C. Cocks, An Identity-Based Encryption Scheme Based on Quadratic Residues, available at http://www.cesg.gov.uk/technology/id-pkc/media/ciren.pdf; D. Boneh, M. Franklin, Identity Based Encryption from the Weil Pairing, ADVANCES IN CRYPTOLOGY—CRYPTO 2001, Lecture Notes in Computer Science 2139 (2001), Springer, 213-229; and D. Boneh, M. Franklin, Identity Based Encryption from the Weil Pairing (extended version), available at http://www.cs.stanford.edu/˜dabo/papers/ibe.pdf. Cocks's scheme is based on the “Quadratic Residuosity Problem,” and although encryption and decryption are reasonably fast (about the speed of RSA), there is significant message expansion (i.e., the bit-length of the ciphertext is many times the bit-length of the plaintext). The Boneh-Franklin scheme bases its security on the “Bilinear Diffie-Hellman Problem,” and it is quite fast and efficient when using Weil or Tate pairings on supersingular elliptic curves or abelian varieties.
However, the known identity-based encryption schemes have a significant shortcoming—they are not hierarchical. In non-identity-based public key cryptography, it has been possible to have a hierarchy of CAs in which the root CA can issue certificates for other CAs, who in turn can issue certificates for users in particular domains. This is desirable because it reduces the workload on the root CA. A practical hierarchical scheme for identity-based cryptography has not been developed.
Ideally, a hierarchical identity-based encryption scheme would involve a hierarchy of logical or actual PKGs. For instance, a root PKG may issue private keys to other PKGs, who in turn would issue private keys to users in particular domains. It also would be possible to send an encrypted communication without an online lookup of the recipient's public key or lower-level public parameters, even if the sender is not in the system at all, as long as the sender obtained the public parameters of the root PKG. Another advantage of a hierarchical identity-based encryption scheme would be damage control. For instance, disclosure of a domain PKG's secret would not compromise the secrets of higher-level PKGs, or of any other PKGs that are not direct descendents of the compromised domain PKG. The schemes taught by Cocks and Boneh-Franklin do not have these properties.
A secure and practical hierarchical identity-based encryption scheme has not been developed. A hierarchical identity-based key sharing scheme with partial collusion-resistance is given in G. Hanaoka, T. i, Y. Zheng, H. Imai, An Efficient Hierarchical Identity-Based Key-Sharing Method Resistant Against Collusion Attacks, ADVANCES IN CRYPTOGRAPHY—ASIACRYPT 1999, Lecture Notes in Computer Science 1716 (1999), Springer 348-362; and G. Hanaoka, T. Nishioka, Y. Zheng, H. Imai, A Hierarchical Non-Interactive Key-Sharing Scheme With Low Memory Size and High Resistance Against Collusion Attacks, to appear in THE COMPUTER JOURNAL. In addition, an introduction to hierarchical identity-based encryption was provided in J. Horwitz, B. Lynn, Toward Hierarchical Identity-Based Encryption, to appear in ADVANCES IN CRYPTOGRAPHY-EUROCRYPT 2002, Lecture Notes in Computer Science. Springer. Horwitz and Lynn proposed a two-level hierarchical scheme with total collusion-resistance at the first level and partial collusion-resistance at the second level (i.e., users can collude to obtain the secret of their domain PKG and thereafter masquerade as that domain PKG). However, the complexity of the Horwitz-Lynn system increases with the collusion-resistance at the second level, and therefore that scheme cannot be both practical and secure.
Accordingly, there has been a need for a secure and practical hierarchical identity-based encryption scheme. It is therefore an object of the present invention to provide a secure and practical hierarchical identity-based encryption scheme. It is another object of the present invention to provide a secure and practical hierarchical identity-based signature scheme. It is a further object of the present invention that the encryption and signature schemes be fully scalable. It is a still further object of the present invention that the encryption and signature schemes have total collusion resistance on an arbitrary number of levels, and that they have chosen-ciphertext security in the random oracle model.